---

Complex visual effects such as caustics are often produced by light paths containing multiple consecutive specular vertices (dubbed specular chains), which pose a challenge to unbiased estimation in Monte Carlo rendering. In this work:

• We analyze light transport behavior within sub-paths containing specular chains and non-specular separators.
• We leverage specular manifolds to reconstruct continuous energy distributions from historical/coherent sub-paths.
• We propose manifold path guiding, a progressive pipeline to importance sample paths with long specular chains via seed chain generation and manifold walks.

Our method achieves up to 40× variance reduction compared to state-of-the-art unbiased methods, particularly in scenes with long specular chains and complex visibility.

Limitations of Existing Approaches

Method	Shortcomings
MLT-based	Struggles with SDS paths despite specialized mutations.
Fitted Distributions	Fail for pure specular cases (e.g., near point lights).
Specular Manifold Sampling (SMS)	Performance degrades for long chains; ignores energy distributions.

Our Solution: Manifold Path Guiding

• Importance sample seed chains in a continuous space, then refine via manifold walks to converge to admissible chains.
• Exploit coherence in specular manifolds along with dimensionality reduction.
• Use converged distributions for efficient rendering.

Key Figures

Citation

@article{Fan23MPG,
  title     = {Manifold Path Guiding for Importance Sampling Specular Chains},
  author    = {Fan, Zhimin and Hong, Pengpei and Guo, Jie and Zou, Changqing and Guo, Yanwen and Yan, Ling-Qi},
  journal   = {ACM Trans. Graph.},
  volume    = {42},
  number    = {6},
  year      = {2023},
  month     = {Dec},
  issue_date= {December 2023},
  articleno = {257},
  numpages  = {14}
}